I have created a linear direct integration time history load case, which contains a bridge live load pattern. This load pattern has a time history function associated.

The problem is that when I change the time history function, all the results stay the same...Even if I create a null time history function (all zeros throughout the time), I still get stresses and deformations in the structure, suggesting that the time history function is actually doing nothing!

Am I doing something wrong? Is this a bug? I've seen that time history functions work with static load cases...Can't it work with moving load cases?

I think u should create moving load case that is presented as multi step static case. I know SAP2000 having this capabilities. In case you are interested in moving load dynamics i guess you should find other advanced software than SAP2000 as the equation of motion for dynamic interaction between vehicle and structure is quite complicated.